July 31, 2020

GENERAL NEW JERSEY MUNICIPAL MONEY MARKET FUND, INC.

Supplement to Summary Prospectus and Prospectus

The Board of Directors of General New Jersey Municipal Money Market Fund, Inc. (the “Fund”) has approved the liquidation of the Fund, effective on or about September 11, 2020 (the “Liquidation Date”).  Before the Liquidation Date, and at the discretion of Fund management, the Fund's portfolio securities will be sold and the Fund may cease to pursue its investment objective and policies.  The liquidation of the Fund may result in one or more taxable events for shareholders subject to federal income tax.  

Accordingly, effective on or about August 31, 2020 (the “Closing Date”), the Fund will be closed to any investments for new accounts, except that new accounts may be established for “sweep accounts” and by participants in group retirement plans if the Fund is established as an investment option under the plans before the Closing Date.  The Fund will continue to accept subsequent investments until the Liquidation Date, except that subsequent investments made by check or pursuant to TeleTransfer or Automatic Asset Builder no longer will be accepted after August 31, 2020.  However, subsequent investments by Individual Retirement Accounts and retirement plans sponsored by BNY Mellon Investment Adviser, Inc. or its affiliates (together, “BNYM Adviser Retirement Plans”) pursuant to TeleTransfer or Automatic Asset Builder (but not by check) will be accepted after August 31, 2020.  Please note that checks presented for payment to the Fund’s transfer agent pursuant to the Fund’s Checkwriting Privilege on or after the Liquidation Date will not be honored.

Fund shares held on the Liquidation Date in BNYM Adviser Retirement Plans will be exchanged for Dreyfus Class shares of General Government Securities Money Market Fund (“GGSMMF”).  Investors may obtain a copy of the Prospectus of GGSMMF by calling 1-800-373-9387.